>Dear all,
>I am new with mathematica. I would be grateful if >someone could tell
>me how can I find the general solutions of the r for the >following
>function f(r_) = 14.4* ((2/Sqrt[r^2 + R^2]) - 1/r ) >(where
>R=constant). I just want to express the function as r >=.....*f. Is
>this possible with mathematica.
>Thank you.
f = 14.4*(2/sqrt(r^2+R^2)-1/r)
-> f/14.4*r*sqrt(r^2+R^2)=2*r-sqrt(r^2+R^2)
-> (f/14.4*r+1)*sqrt(r^2+R^2)=2*r
-> (f/14.4*r+1)^2*(r^2+R^2)=4*r^2
-> ...
-> r^4+2/y*r^3+(R^2-3*(14.4/y)^2)*r^2+2/y*R^2*r+...
...+(14.4/y)^2*R^2 = 0
This is a quartic polynomial equation.
Take a look at
http://reference.wolfram.com/mathematica/tutorial/NumericalSolutionOfPolynomialEquations.html
how to solve them analytically and numerically in
Mathematica.
Be careful: maybe not all solutions of the polynomial equation will be solutions of your original equation.
Best wishes
Torsten.